Abstract
Let
be a commutative ring with identity and
be a multiplicative subset of
. In this paper, we introduce the concept of weakly
-prime ideals which is a generalization of weakly prime ideals. Let
be an ideal of
disjoint with
. We say that
is a weakly
-prime ideal of
if there exists an
∈
such that, for all
∈
, if 0 ≠
∈
, then
∈
or
∈
. We show that weakly
-prime ideals have many analog properties to these of weakly prime ideals. We also use this new class of ideals to characterize
-Noetherian rings and
-principal ideal rings.